Convergent or Divergent Series

For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example.

**A.** The series is absolutely convergent.

**B.** The series converges, but not absolutely.

**C.** The series diverges.

**D.** The alternating series test shows the series converges.

**E.** The series is a \(p\)-series.

**F.** The series is a geometric series.

**G.** We can decide whether this series converges by comparison with a \(p\) series.

**H.** We can decide whether this series converges by comparison with a geometric series.

**I.** Partial sums of the series telescope.

**J.** The terms of the series do not have limit zero.

**K.** None of the above reasons applies to the convergence or divergence of the series.

f(n)=cos^2(npi)/(npi)

n from 1 to infinity

I know it is divergent by harmonic series, however CK is not the correct answer.

Re: Convergent or Divergent Series

Quote:

Originally Posted by

**kjnabs** For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example.

**A.** The series is absolutely convergent.

**B.** The series converges, but not absolutely.

**C.** The series diverges.

**D.** The alternating series test shows the series converges.

**E.** The series is a \(p\)-series.

**F.** The series is a geometric series.

**G.** We can decide whether this series converges by comparison with a \(p\) series.

**H.** We can decide whether this series converges by comparison with a geometric series.

**I.** Partial sums of the series telescope.

**J.** The terms of the series do not have limit zero.

**K.** None of the above reasons applies to the convergence or divergence of the series.

f(n)=cos^2(npi)/(npi)

n from 1 to infinity

I know it is divergent by harmonic series, however CK is not the correct answer.

I really do not know exactly how to read the above.

That said, the series $\displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\cos }^2}(n\pi )}}{{n\pi }}} = \sum\limits_{n = 1}^\infty {\frac{1}{{n\pi }}}$ **diverges**.

So the answer is **C.** The series diverges. Why do you doubt that answer?

Re: Convergent or Divergent Series

CG is the correct combination, the harmonic series is a p series with p = 1

Re: Convergent or Divergent Series

Quote:

Originally Posted by

**agentmulder** CG is the correct combination, the harmonic series is a p series with p = 1

Frankly, if I were you I would get out of what ever course this come from.

Because, if you want to learn mathematics that kind of nonsense is going to handicap you.

Re: Convergent or Divergent Series

I only got partial marks on the problem and I was pretty sure that that was the question I was getting wrong, the other questions are as follow, I may have gotten one of them wrong

(2n+2)!/(n!)^2

cos(npi)/(npi)

1/(n^(3/2))

1/(nlog(3+n))

(6+sin(n))/(n^(1/2))

I'm pretty sure the answers are as followed CJ, BD, AE, CK, CG,

Re: Convergent or Divergent Series

What is wrong with what i said?

Re: Convergent or Divergent Series